{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **演示0302：概率模型及其分布**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### **基本概念**\n",
    "* **随机试验(random experiment)**：在相同条件下对某随机现象进行的大量重复观测\n",
    " * 例如：抛硬币、丢骰子等\n",
    "* **随机事件(random event)**：在随机试验中，可能出现也可能不出现，而在大量重复试验中具有某种规律性的事件\n",
    " * 例如：抛硬币扔出的结果是正面，丢骰子扔出的的结果是5点等\n",
    "* **概率**：表示在某些给定条件下，随机事件$A$发生的可能性，记为：$P(A)$\n",
    "* 随机变量(random variable)：表示随机试验各种结果的实值单值函数。它是从样本空间的子集到实数的映射，将事件转换成一个数值，从而便于数学运算\n",
    " * 例如：使用变量来表示抛硬币的结果，如果是正面，则用1表示，概率记为$P(A=1)$，或$P(A_1)$；如果是背面，则用0表示，概率记为$P(A=0)$，或$P(A_0)$\n",
    " * 又如：使用变量来表示丢骰子的结果，各种结果的概率可分别表示为：$P(A=1),P(A=2),P(A=3),P(A=4),P(A=5),P(A=6)$\n",
    "* 随机变量的类型：\n",
    " * **离散型随机变量(discrete random variable)**：取值是可数个值的随机变量。例如，表示抛硬币、丢骰子的随机标量\n",
    " * **连续型随机变量(continuous random variable)**：取值是一个区间中的任意一点(也就是不可数)的随机变量，比如人的身高、商品价格等\n",
    "* **概率质量函数(Probability Mass Function, PMF)**：离散型随机变量在各特定取值上的概率，其值本身就是概率\n",
    "* **概率密度函数(Probability Density Function, PDF)**：连续型随机变量在某个确定的取值点附近的可能性，但是：\n",
    " * PDF本身并不是概率值，而是需要在一定区间积分后才是概率值\n",
    " * 连续型随机变量在某个点的概率为0(虽然其PDF值并不为0)\n",
    "* **累积分布函数(Cumulative Distribution Function, CDF)**\n",
    " * 反映了随机变量到当前指定值为止的所有概率之和。其值域为$[0,1]$\n",
    " * 对于连续型随机变量：$ CDF(x) = \\sum_{t=-\\infty}^{x}PDF(t)dt $\n",
    " * 对于离散型随机变量：$ CDF(x) = \\sum_{k=1}^{x}PMF(k) $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### **案例1：离散型随机变量的概率分布**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ">**0-1分布**  \n",
    "* 某个事件只有两种结果：发生或不发生，而且该事件每次发生的概率都是$p$\n",
    "* 伯努利实验：在同样的条件下，重复、独立的进行的随机实验；实验只有两种结果。0-1分布就是对伯努利实验的描述\n",
    "* 概率质量函数：$ P(x_k)=p^k (1-p)^{(1-k)} $，其中，$k=0或1$，$x_0$表示该事件不发生的情形，$x_1$表示该事件发生的情形\n",
    "* 以丢硬币为例，扔出结果为正面(可视为：事件发生)的概率为$p=50\\%$，扔出结果为背面(可视为：事件不发生)的概率为：$p=50\\%$；各次试验是独立的伯努利实验"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> **几何分布**\n",
    "* 在$n$次伯努利实验中，实验$k$次才得到第一次成功的机率，即：前$k-1$次都失败，第$k$次成功的概率\n",
    "* 概率质量函数：$ P(x_k)=(1-p)^{(k-1)} \\cdot p $，其中，$p$是单次实验中，发生该事件的概率\n",
    "* 仍以丢硬币为例，假设要计算丢3次硬币才得到1次正面结果的概率，则为：$P(x_3)=(1-p)^{(3-1)} \\cdot p=(1-0.5)^2*0.5=0.125$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ">**二项分布**\n",
    "* 重复$n$次伯努利实验，在$n$次实验中，发生$k$次事件的概率\n",
    "* 概率质量函数：$ P(x_k)=C_n^k p^k (1-p)^{(n-k)} $，其中，$p$是单次实验中，发生该事件的概率。$ C_n^k=\\dfrac{(P_n^k)}{k!}=\\dfrac{n!}{k!(n-k)!} $\n",
    "* 仍以丢硬币为例，假设要计算扔10($n$)次硬币，其中5($k$)次为正面的概率，则为：$ P(x_5)=C_{10}^5 * p^5 * (1-0.5)^{(10-5)} = \\dfrac{10!}{5!*(10-5)!}*0.5^5*0.5^5=0.246$\n",
    "* *scipy.stats.binom.pmf(k, n, p)*方法提供了计算二项分布概率的实现。上面的例子可以写为："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.24609375000000025\n"
     ]
    }
   ],
   "source": [
    "''' 使用scipy.stats.binom.pmf计算二项分布的概率 '''\n",
    "\n",
    "import numpy as np\n",
    "import scipy.stats as sps\n",
    "\n",
    "n = 10\n",
    "p = 0.5\n",
    "k = 5\n",
    "print(sps.binom.pmf(k, n, p))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ">**二项分布的另一个例子**\n",
    "假设某人投篮命中率为0.3，总共投篮10次，问至少投中2次的概率？  \n",
    "* 分析：每次投篮有2种结果，投中或未中；每次投中概率相同(0.3)，每次投篮可认为独立事件。因此符合二项分布\n",
    "* 至少投中2次的概率：$ P(x \\geq 2)=P(x_2)+P(x_3)+P(x_4)+\\cdots+P(x_{10}) $\n",
    "* 计算方法如下："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8506916540999998\n"
     ]
    }
   ],
   "source": [
    "''' 使用scipy.stats.binom.pmf计算二项分布的概率 '''\n",
    "\n",
    "n = 10\n",
    "p = 0.3\n",
    "k = np.arange(n+1)\n",
    "p_series = sps.binom.pmf(k, n, p)\n",
    "print(sum(p_series[2:]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ">**泊松分布**\n",
    "* 日常生活中，大量事件是有固定频率的，比如：\n",
    " * 某医院平均每小时出生3个婴儿\n",
    " * 某网站平均每分钟有2次访问\n",
    " * 某超市平均每小时销售4包奶粉等  \n",
    "* 它们的特点是，我们可以预估这些事件的总数，但是没法知道具体的发生时间。例如：平均每小时出生3个婴儿，但无法准确得知下一个小时会出生几个。泊松分布就是描述某段时间内，事件具体的发生概率\n",
    "* 概率质量函数：$ P(N(t)=n)=\\dfrac{(\\lambda t)^n e^{-\\lambda t}}{n!} $\n",
    " * $N$表示某种函数关系，$t$表示时间(为单位时间的倍数)，$\\lambda$表示事件的平均频率(已知)，$n$表示待计算的事件次数。\n",
    " * 例如，如果平均每小时出生3个婴儿，则$\\lambda=3$，以1小时为单位时间。\n",
    "* 泊松分布示例：\n",
    " * 计算：1小时出生3个婴儿的概率。此时，$n=3,t=1,P(N(1)=3)=\\dfrac{(3 \\cdot 1)^3 e^{-3 \\cdot 1}}{3!}\\approx 0.224$\n",
    " * 计算：接下来2个小时，一个婴儿都不出生的概率。此时，$n=0,t=2, P(N(2)=0)=\\dfrac{(3 \\cdot 2)^0 e^{(-3 \\cdot 2)}}{0!} \\approx 0.0025$\n",
    " * 计算：接下来1个小时，至少出生2个婴儿的概率。$P(N(1) \\ge 2)=1-P(N(1)=0) - P(N(1)=1) = 0.8 $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### **案例2：连续型随机变量的概率分布**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ">**均匀分布**\n",
    "* 该随机变量所有可能值的出现概率相同。\n",
    "* 概率密度函数： $ PDF(x)=\\dfrac{1}{b-a},(a \\leq x \\leq b) $，假设该随机变量的取值范围在$[a, b]$区间\n",
    "* 累积分布函数：$ CDF(x)=\n",
    "\\left\\{\n",
    "\\begin{aligned}\n",
    "&\\dfrac{x-a}{b-a},& (a \\leq x \\leq b) \\\\\n",
    "&0, & (x \\lt a) \\\\\n",
    "&1, & (x \\gt b)\n",
    "\\end{aligned}\n",
    "\\right. $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ">**指数分布**\n",
    "* 泊松分布是单位时间内独立事件发生次数的概率分布，指数分布是独立事件的时间间隔的概率分布，或者说某个事件在时间($x$)内发生的概率\n",
    "* 概率密度函数： $ PDF(x)=\\lambda e^{-\\lambda x},(x>0) $。其中，$\\lambda$称为率参数(rate parameter)，即单位时间内发生事件的次数（频率）\n",
    " * 另一种写法：$ PDF(x)=\\dfrac{1}{\\theta} e^{\\frac{-x}{\\theta}}, (x>0) $。其中，$ \\theta=\\frac{1}{\\lambda} $\n",
    "* 累积分布函数：$ CDF(x)=1-e^{-\\lambda x} $。注意，该函数是概率密度函数的积分\n",
    "* 指数分布示例\n",
    " * 之前泊松分布中的例子，假设平均每小时出生3个婴儿($\\lambda=3$)，并且刚才过去的那个小时正好已经生了3个婴儿，那么接下来的15分钟，有婴儿出生的概率是多少？\n",
    " * 以小时为单位，15分钟为0.25小时，使用累积分布函数来计算0~0.25小时区间内事件出现的概率：$ CDF(0.25)=1-e^{-\\lambda x}=1-e^{-3 \\cdot 0.25} \\approx 0.53 $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ">**正态分布**\n",
    "* 正态分布又叫高斯分布。对于服从$N(\\mu,\\sigma^2)$的正态分布，$\\mu$决定了正态分布中心线的位置，$\\sigma$决定了它的幅度。\n",
    "* 概率密度函数：$ PDF(x)=\\dfrac{1}{\\sigma \\sqrt{2\\pi}} e^{-\\frac{(x-\\mu)^2}{2\\sigma^2}} $\n",
    " * *scipy.stats.norm.pdf(x, mu, sigma)*方法提供了计算正态分布概率密度函数的实现\n",
    "* 标准正态分布：$\\mu=0,\\sigma^2=1$时，被称为标准正态分布。此时：\n",
    " * 函数曲线下68.268949%的面积在平均值左右的一个标准差范围内\n",
    " * 95.449974%的面积在平均值左右两个标准差2σ的范围内\n",
    " * 99.730020%的面积在平均值左右三个标准差3σ的范围内\n",
    " * 99.993666%的面积在平均值左右四个标准差4σ的范围内\n",
    "* 累积分布函数：$ CDF(x)= \\frac{1}{\\sigma \\sqrt{2\\pi}} \\int_{-\\infty}^{x} e^{-\\frac{(x-\\mu)^2}{2\\sigma^2}}dx $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Ll6e1Ji2vosO7L7Wmfw8tIObt7U1BQYEkeDvSWlNQUIC3t3eH+5BpGeHyCipqKa8xE2fjnZMSwv1YszOLqtp6fDw7Vh++O4qOjiYzMxPZKtO+vL29iY6O7vD9JbkLl5deWAl0fPel1sSEGv1lFlUyMCrApn07Mw8PD+Lj4x0dhmiHVdMySqmZSqlDSqlUpdTiVtpcr5Q6oJTar5Rabtswhei4jIbkHhNin+Te+OEhhDNpd+SulHIDXgWmY2yWvV0ptU5rfaBZm4HAI8D5WusipVTPWvgrnFp6gZF8o22c3GMluQsnZs3IfQKQqrVO01rXAiuAM8+VvRN4VWtdBKC1zrVtmEJ0XEZRJZEBXjafFw/z88TX042MQjlLVTgfa5J7XyCj2eXMhuuaGwQMUkp9q5T6QSk101YBCtFZ6YWVTaNsW1JKERvqKyN34ZSsSe4tVUU6cw2UOzAQmAIsAJYqpYLP6kipRUqpZKVUshxpF10lo7CqaX7c1qJDfJvm9IVwJtYk90ygeSm9aCC7hTYfaa3rtNbHgEMYyf40WuslWuskrXVSRERER2MWwmq1ZgvZJfZL7o0jd1nzLZyNNcl9OzBQKRWvlPIE5gPrzmizFpgKoJQKx5imSbNloEJ0RHZxFVpjl2kZgNhQH6rq6imosP0Gx0J0RrvJXWttBu4FNgIHgZVa6/1KqSeVUnMamm0ECpRSB4DNwG+11gX2CloIazXOh9stuYfJihnhnKw6iUlrvR5Yf8Z1jzf7XQMPNvwI4TTsntwb+s0orGRsrG12eRLCFqS2jHBpGYWVeLqbOr0pdmsa1843rqUXwllIchcuLb2wkugQH7ttheft4UZkgJdMywinI8lduLSMIvuscW8uNtSXjCJJ7sK5SHIXLi29oIuSu5ylKpyMJHfhskoq6yitNtu8YNiZokN9yS6potZssevjCHEuJLkLl9U4D26vE5gaxYb6ojVkFcvoXTgPSe7CZdl7GWQjqQ4pnJEkd+GyGg9yxoT62PVxmq91F8JZSHIXLiu9sJJQP08CvD3s+jiRAV54upskuQunIslduKyMwkpiQuw7agcwmRTRIT4yLSOciiR34bLSCyvtfjC1kdR1F85GkrtwSfUWTVZRld0PpjaS5C6cjSR34ZJOllRhtuguG7nHhPhSVm2muFJK/wrnIMlduKTGM0btfQJTo8YVOZlFstZdOAdJ7sIlZXbRMshGjdUhM6XGjHASktyFS8ooqkIp6B3UNcm98RuC1JgRzsKq5K6UmqmUOqSUSlVKLW7h9oVKqTyl1O6GnztsH6oQ1sssqqRXoDee7l0zfgn0cSfAy11G7sJptLsTk1LKDXgVmI6xEfZ2pdQ6rfWBM5q+r7W+1w4xCnHOMgurumy+HUApRXSoLxky5y6chDXDmglAqtY6TWtdC6wArrJvWEJ0TmaRsUlHV4oO8ZGRu3Aa1iT3vkBGs8uZDded6Rql1F6l1CqlVExLHSmlFimlkpVSyXl5eR0IV4j21Zot5JRWE91FyyAbxYT4kllUhbGlsBCOZU1yb2l/sjNfvR8DcVrrkcAXwDstdaS1XqK1TtJaJ0VERJxbpEJY6WRJFRaNQ0bulbX1FFbIWnfheNYk90yg+Ug8Gshu3kBrXaC1rmm4+CYwzjbhCXHuGtead+WcO/xUN17WugtnYE1y3w4MVErFK6U8gfnAuuYNlFK9m12cAxy0XYhCnJvG6oyOGLkDsp+qcArtrpbRWpuVUvcCGwE34C2t9X6l1JNAstZ6HXC/UmoOYAYKgYV2jFmINmUWVeFmUvQO8u7Sx21M7jJyF86g3eQOoLVeD6w/47rHm/3+CPCIbUMTomMyiirpHeSNu1vXnqMX4O1BsK+H1HUXTkHOUBUuJ7OoqsunZBoZyyFl5C4cT5K7cDnGJh1dezC1UUyIr8y5C6cgyV24lOq6enLLapoKeXW16BAfsmStu3ACktyFS8kublgG2UXVIM8UE+pLjdlCXnlN+42FsCNJ7sKlNNZ2ceTIHaQ6pHA8Se7CpXR1HfczxUhdd+EkJLkLl5JRWIWHmyIyoGvXuDfqK2vdhZOQ5C5cSmZRJX2CfXAztVQSyf58Pd0J8/OUkbtwOEnuwqVkFHVtHfeWRIf6ypy7cDhJ7sKlZDmgjvuZpK67cAaS3IXLqKqtJ7+8tqk6o6PEhPiSVVyFxSJr3YXjSHIXLqNxtOwMI/e6es2psmqHxiF6NknuwmVkNC2DdOzIPbbh8WXeXTiSJHfhMtILjOQe6yTJPV2qQwoHkuQuXEZ6YRU+Hm6E+Xk6NI4+wT4oJcldOJYkd+Ey0gsriQ31RSnHrHFv5Oluok+Qj9R1Fw5lVXJXSs1USh1SSqUqpRa30e5apZRWSiXZLkQhrJNZVOnw+fZGMaE+MnIXDtVucldKuQGvApcDw4AFSqlhLbQLAO4Htto6SCHao7VuGrk7g9hQXxm5C4eyZuQ+AUjVWqdprWuBFcBVLbT7E/A3QNZ/iS5XUFFLZW09sZ0pGGaph5qyn34s9R3uKjbUl9yyGqpqO96HEJ1hzR6qfYGMZpczgYnNGyilxgAxWutPlFIPtdaRUmoRsAggNjb23KMVohWNUyDnPC1jroG0LXDgI0j5FKqLf7rNNwyGzIZhV0H8ReDmYXW3jXFkFlUyMCrg3GISwgasSe4tHZ1qOvVOKWUCXgAWtteR1noJsAQgKSlJTt8TNtM4BXJO0zIpn8Knv4Gyk+AVBENmQeQwUAq0hpN74MfVsPMdCI6F2f+AAdOs6jqm2XJISe7CEaxJ7plATLPL0UB2s8sBwHBgS8MqhV7AOqXUHK11sq0CFaItjcndqk06ynNh/W/hwFqIGg5XvggJU8G9hSWUddWQ+l/48kn499UwagHM+DP4hrb5ELLWXTiaNcl9OzBQKRUPZAHzgRsbb9RalwDhjZeVUluAhySxi66UXlhJZIAXPp5ubTc8uQfevRpqSuGSx+D8X7c93eLhDUOvhAHT4etn4dt/QNpXcMtaiBjc6t3C/Dzx9XST5C4cpt0DqlprM3AvsBE4CKzUWu9XSj2plJpj7wCFsEZ6oRXLINN/gLevBHdv+MXXcNFvrZ9H9/CGaX+AO74Eixn+73LI3t1qc6UUMSFS+lc4jlXr3LXW67XWg7TW/bXWTzdc97jWel0LbafIqF10tYzCqrbn249ugnfngV843PYZRA7t2AP1GW3c38MX3rkSTnzfatMYWQ4pHEjOUBXdXq3ZwsmSqtZH7pnJsHw+hCYYiTk4puV21grrb/TjHwn/vgZyfmyxWWyoL+mFlWgtawdE15PkLrq97OIqLLqVlTIlWbDiRgjsDbesMxKyLQRFw62fgHcg/GcBVOSf1SQ21IeqOqPGvBBdTZK76PbSW1sGWVtpJPbaSliwAvzCbPvAgb1h/nKoyIX3bwbz6Uk8NkxWzAjHkeQuur2fTmBqdnaq1rDuXmN1zDVLOz7H3p6+Y+GqVyH9O1h/+vl7jXu5yry7cARJ7qLbyyisxNPNRFSA909X7nzHOAFp2uMweKZ9AxhxLVzwoPGY+1Y1XR0tyV04kCR30e1lFFUSHeqDydRwMnVhGnz2e4i/2FjH3hWmPgp9k+DTB6HUOMfPx9ONyAAvmZYRDiHJXXR7p1WDtNTDh3eDyR3mvgamLnqJu7nDvDeMefePfmlMC/HTihkhupokd9HtpRc0S+7fvQQZP8CsZ40VLV0pfABc9idjTf32pYCU/hWOI8lddGsllXWUVpuNg5e5KbDpaaOK48jrHRPQ+Dug/zT4/A9QeIzoUF9OllZTY5bSv6JrSXIX3VpGUcNKmRAfo8Kjlz9c8bxR2dERlII5L4MywYaHiQ3xQWvIKpIyBKJrSXIX3dqx/AoARhRuhBPfwLQ/GiUGHCmoL0xZDEc2MrryWwBOFMjUjOhaktxFt3Y8v4JAKuiz9SnoOw7G3urokAyT7oaIocQnP4UP1U0fQkJ0FUnuols7ll/B475rUFUFxnRMV62OaY+bB8x+HrfSDB70XifJXXQ5J3knCNEx+uRerrZsNA5k9hnt6HBO1+88GLWAhXxC1clDjo5G9DCS3EX3pTULiv9JlVuAcRKRM5r+JPUmT67Me8PRkYgeRpK76LbK933KBPazp/8vwCfY0eG0zD+SHTELudiylZrUrx0djehBrEruSqmZSqlDSqlUpdTiFm6/Sym1Tym1Wyn1jVJqmO1DFaKZejNuXz7OUUtvakY7yUHUVhSNuJ1sHYpl42NgsTg6HNFDtJvclVJuwKvA5cAwYEELyXu51nqE1no08DfgeZtHKkRzO9/Gp+QofzEvIC4yxNHRtKlfrwierbsBn7w98OOq9u8ghA1YM3KfAKRqrdO01rXACuCq5g201qXNLvoBsvWMsJ/qUtj8DBkBY9hMEtEhPu3fx4Hiwn1ZazmfPP8h8MX/gzo5oUnYnzXJvS+Q0exyZsN1p1FK/VIpdRRj5H5/Sx0ppRYppZKVUsl5eXkdiVcI+O5lqMznveBFxIT64eHm3IeOArw9CPP3YXX43VCaCdvedHRIogew5l3R0nncZ43Mtdavaq37Aw8Dj7XUkdZ6idY6SWudFBERcW6RCgFQngffvwrD5vJVeQzx4X6OjsgqCeF+fFk9CAZcCt88D9Uljg5JuDhrknsm0HxH4Wggu432K4C5nQlKiFb97+9grsIy5VGO51d0m+QeH+5nnMh0yR+gqgi+e8XRIQkXZ01y3w4MVErFK6U8gfnAuuYNlFIDm128AjhiuxCFaFCcAcnLYPSNnPKKoaquvvsk9wg/8strKQ1NhGFzjW8f5TI1Keyn3eSutTYD9wIbgYPASq31fqXUk0qpOQ3N7lVK7VdK7QYeBJx7bZronr76i/HvxYs5lmeczp/QXZJ7Q5zH8yvgksfAXGVMzwhhJ+7WNNJarwfWn3Hd481+/5WN4xLidHmHYfdymHgXBMdw7NAJAOK6WXI/ll/ByNEDYfSNxoYek+6B4Jh27i3EuXPuZQZCNNryDLj7GBtRA8fyKvD2MNEr0LudOzqH2FBflIK0hm8cXNxwLuDXzzouKOHSJLkL53dqP+z/ECbdBf7GKqtj+RXEhfn9tCm2k/P2cKNvsA/HCxqSe3AMjFsIu9+DwmMOjU24JknuwvlteQa8AmDyvU1XHcuvICGie0zJNGpaMdPoggeNjbxl9C7sQJK7cG4n98DBj425ad9QAMz1FtILK4kL64bJPa8CrRtOEwnsDUm3w57/QH6qY4MTLkeSu3BuW/4C3kHGzkYNMouqMFt0t1kG2Sg+3I+yGjMFFbU/XXnBr8HdG776q+MCEy5JkrtwXlk74NB6OO++00r6Nk5tdMfkDs0OqgL4R8KEO2HfB5Cb4qDIhCuS5C6c1+ZnwCfEWP7YzKFTZQAMjAxwRFQdNiDSH4DDDfE3Oe9X4On30zp+IWxAkrtwThnbIfW/cP6vjIOpzRzOKaNXoDdBvh4OCq5j+gb7EODlfnZy9wuDib+A/WuNlUFC2IAkd+GctvwZfMNg/J1n3ZSSU8bgXt1r1A6glGJQrwBScsrOvnHyveDpbxxjEMIGJLkL55P+AxzdBOf/Grz8T7vJXG8hNa+8WyZ3gEFRARzKKftpxUwj31DjoPHBdZCzzzHBCZciyV04n81/Br8IGH/7WTcdL6ig1mxhcFT3TO5DegVQUlXHqdKas2+cfA94BcnoXdiEJHfhXE58B8e+ggseMA4ynqFxSqO7jtwb407JKT37Rp8QI8GnfALZu7s4MuFqJLkL56E1bHoa/KMg6bYWmxzOKcPNpJpWnnQ3QxqS+1kHVRtNuttY17/lmS6MSrgiSe7CeRz7Ck58Axf+Bjxa3hc1JaeMuDBfvD3cujg42wj29SQq0Kvlg6pgJPbz7oPDn0Hmjq4NTrgUSe7COTSO2gP7wtjWtwM4dKp7rpRprvGgaqsm3gU+obD56a4LSrgcq5K7UmqmUuqQUipVKbW4hdsfVEodUErtVUp9qZTqZ/tQhUtL/QIyt8FFD4FHy2V8K2vNpBdWMjgqsIuDs60hvQI4kluOud7ScgOvAKMswdEvjZVDQnRAu8ldKeUGvApcDgwDFiilhp3RbBeQpLUeCawC/mbrQIUkolLTAAAgAElEQVQL09oYpQbHwuibWm12+FQ5Wnffg6mNBvcKpNZs4XhBZeuNxt8JfpGw6amuC0y4FGtG7hOAVK11mta6FmMD7KuaN9Bab9ZaN75Sf8DYRFsI6xxaD9m74OKHwd2z9WYNK0yGdPPk3hh/m1Mznr5w4YNw/H+Q9lUXRSZciTXb7PUFMppdzgQmttH+dmBDZ4ISPYjFYsy1hybAyPltNj2UU463h4nYUN8OP5zWmuKaYvKr8imqLqKwppCK2gqqzFVU11djtpib2rqb3PFx98HbzRt/T39CvUMJ8Qoh3CecIK8glOrYRiEDIv0xKeP4wRX0br3huJ/Dty8Zo/f4i6CDjyd6JmuSe0uvKN3CdSilbgKSgItbuX0RsAggNjbWyhCFS/txFeTuh2uWgVvbL8dDp0oZFBVg1e5LlXWVHC46zNHio6SVpHGs5BiZ5ZnkVORQZa7qdNg+7j708etDdEA08UHxJAQl0D+4P4NCBuHt3vbWf94ebsSF+TV9E2mVhzdc/Dv45NfG6pnBl3c6btFzWJPcM4HmO/hGA9lnNlJKXQo8ClystW7h9DvQWi8BlgAkJSW1+AEhehBzrTHXHjUCEq9ut/mhnDKmDo4863qtNcdKjrEjdwe7c3ezP38/x0qPYdHGAUsvNy/ig+LpH9SfC/teSG+/3oT7hhPqFUqIdwgBngHGCN3dG3f101vCrM1U1Rkj+tLaUoqqiyiqLiKvKo/s8mxOVpwkvSyd77O/p9Zi1Gh3U24kBCeQGJbImMgxjI0cS7/AfmeN8gf3CuDgyXaSO8CYm+C7l+DLP8HAGWCSBW7COtYk9+3AQKVUPJAFzAdubN5AKTUGeAOYqbXOtXmUwjXt+hcUHYcbV7abtPLLa8gvr206mHqy/CTfn/ye77K/Y9vJbRTVFAEQ6h3K8PDhTI+bzrDQYQwIGUAfvz64mc59Xbwbbni5eQHQy69Xq+3qLfVklWdxpOgI+wv2c6DwAFsytrA2dS0AYd5hTOw9kcl9JjO592Si/KIY3CuAz/bnUFlrxtezjbehmwdMfRRW3258yxl5/Tk/D9EztZvctdZmpdS9wEbADXhLa71fKfUkkKy1Xgc8C/gDHzSMUNK11nPsGLfo7mor4atnIWYSDLys3eYHT5Zg8k7nUM0+5n20ldRiY1u6SJ9ILoy+kKSoJMZEjmlxlGxvbiY3YgNjiQ2MZVq/aQBYtIXjJcfZmbuT5FPJfJ/9PeuPrQdgSOgQor2SUF7BHM4pY3RsSNsPkHg1fPsP41vOsLltHnQWopE6qzpdF0lKStLJyckOeWzhBL55Ab54An6+Afqd12ITi7awN28vG49vZO3hDZTXF2BSboyLGsvF0Rdzfp/z6R/cv8uTeUdYtIUjRUf4Nvtbvsr4it25u7FgIcgjknmDZjEjbgaJYYmtP5fDn8Py62DWc8bOTaLHUkrt0FontdtOkrvocpWF8OJoiJkAN6066+ZjJcf4+OjHrD+2nqzyLDxMHgTqEVQUDeOLu+4iyCvIAUHbVmFVIVNee43wqEMUWX7ErM3EBsQyO2E2sxNmExMYc/odtIb/mwUFR+D+XWdtYCJ6DmuTuzVz7kLY1tfPQm0ZTH+y6aqKugo+O/YZa1LXsDdvLyZlYlLvSfxy9C+ZEjOFGX/fxqS4UJdI7AChPqGMC72MrLwL2XLPaDalb+KTtE94fc/rvLbnNcZGjuWaQdcwvd90fNx9jGWQl/0Jlk4zlkde8qijn4JwcpLcRdcqTINtb8KYmyFqGAcKDrDy0ErWH1tPlbmKhKAEfjPuN8xKmEWkr7EyJqekmuySau6ICW6n8+5lTGwIWw7nobQv8wbOY97AeeRU5PBJ2id8eORDHv3mUZ7Z+gxXJFzB9YOvZ1B0kjH//t3LkPRzCOzj6KcgnJgkd9G1vvh/1Lp5srH/eFZ8+jP25u/F282bmfEzuWbgNYyKGHXWvPOudGMlzJhYV0vuwWgNezKKuXBgBGCsyrljxB3cPvx2kk8ls+bIGj488iHvH3qfsZFjmT90GpemfILH5qfhqlcd/AyEM5PkLrpMfup/eT97Mytj+1KY/DfiAuNYPGExV/a/kkDP1ouB7cooxtPNxLA+3btg2JlGxQSjFOxK/ym5N1JKMb7XeMb3Gs/vxv+Oj1I/YuXhlfxux7NExsVxQ9o6rs24idCYyQ6KXjg7Se7C7o4UHeGd/W+zPnUddSFBXNRrHD9LvIXJvSdbtdJlV3oRw/sG4uXePWu4tybQ24OBkf7sbPhm0poQ7xAWDl/ILYm38E3WN/z7x//jZUs1Szb9gjmDruXmYTcTHxTfRVGL7kKSu7ALrTXbc7bz1v63+DbrW3xMHlxTVsZN439Dv0n3Wd1PXb2FvZkl3DTJNatIj4kJ4bP9OWit2/2gMykTF0VfxEXRF3H0qz/z7r43+ejIh3xw+AOmxEzhtuG3MSZyTBdFLpydnMssbMqiLfz3xH+58dMbuf3z20kpSOG+EYv476kyHvUZQL8Jvzyn/g6eLKXGbHG5+fZGY2KDKamq41h+xTndr/8Fv+MJUy8+LzJz9/A72J27m1s23MItG25hS8YWHLXEWTgPSe7CJuosdaxNXctVa6/iwS0PUlpbyuOTH2fjtRtZlH+KoPI8uPxv51wbZVd6MWCsLHFFjc9rZ8PztJqbO1z+N8KK0rmnvIaN12xk8YTFnKo4xX2b7uOaj6/h07RPT6tyKXoWSe6iU2rqa1iRsoIr1lzBH779A97u3jx78bOsm7uO6wZdh1fhCfjhdRh7M/Qde87970ovIirQiz5BbVda7K4GRvoT4OXetCLonMRfCInz4H/P41uRz8+G/oxPrv6EP1/wZywWC4v/t5g5a+ew+vBq6urrbB+8cGqS3EWHVNZV8s7+d5i5eiZPb32aKN8oXp32Kitnr2Rm3EyjUJfWsOF34OEHlzzeocfZlVHMmJiQblFioCNMJsWomOCmbyjnbPqfjH83/h4AD5MHV/a/kjVXreEfU/9BoGcgT3z/BLM+nMXyg8upqW+xYKtwQZLcxTmpqKtg2b5lzFw9k+eSnyMhKIFlly3jX5f/i4uiLzo9Ce9dCWmbYdofwD+i9U5bkV9ew4mCSpedb280JjaYlJxSKms7MIUSHAMX/xYOfgwp65uuNikT02Kn8Z8r/sM/L/0nvf1688y2Z7h89eX8a/+/bFLTXjg3WS0jrFJWW8Z/Uv7Dvw78i5KaEs7vez53jbyL0ZGjW75DRQFsfASiJ0DSbR16zN0No9mx/Vxzvr3R2NgQLBr2ZJQwuX/YuXdw3v2wbzV8+huIuwC8fzofQCnF+X3P57w+55F8Kpl/7vknzyY/y7Ifl7EwcSE3DL4BX4+O72wlnJeM3EWbSmtLeX3368xYPYOXd73MqIhRLJ+1nH9e+s/WEzsY0wTVpTDnJehALXWAbccL8XBTDO/jGvVkWjO64WSmbccKO9aBmwfMeRnKTsKXT7bYpPGkqGUzlvHOzHcYHDKY53c8z8zVM1m6bykVdee2Wkc4P0nuokUlNSW8susVZqyawWt7XmN81Hjen/0+r057lRERI9q+c+qXsHcFXPAARA7tcAybU3KZEB+Kj6drnbx0phA/T0b2DWLzoU7scxM9DibeBduXQvrWNpuOjRrLksuW8O7l75IYnsiLO19kxuoZLNm7hPLa8o7HIJyKJHdxmqLqIl7a+RIzVs/gjb1vMKn3JD648gNevORFhoUNa7+D6lJjz8+wgXDhbzocR0ZhJUdyy1vcVs8VTR0SyZ7MYgrKO3HA85LHICga1t0Hde3PqY+OHM3rl77O8lnLGRUxipd3vcxlqy/j9T2vU1prxRaAwqlZldyVUjOVUoeUUqlKqcUt3H6RUmqnUsqslLrW9mEKeyuoKuCFHS8wY/UMlu5bynl9zmPVlat4YeoLDAkdYn1Hny2GkkyjqJVHx5cvbmkYxV4ypGck90uGRKI1fHU4r+OdePkb02D5h4yNUKw0ImIEr057lRWzVzAuahyv7X6NGatm8MquVyipKel4PMKh2j2gqpRyA14FpmNslr1dKbVOa32gWbN0YCHwkD2CFPaTV5nH2/vfZuWhldTU1zAzfiaLRixiQMiAc+/swDrY/R5c9FuIndipuDal5NIvzJf4cL9O9dNdDO8TRLi/F5sP5XH12OiOd9T/EmN6Zus/YdAM47KVEsMSefmSlzlYcJAle5fwxt43ePfAuywYsoBbEm8h1Du043GJLmfNapkJQKrWOg1AKbUCuApoSu5a6+MNt1nsEKOwg5PlJ3nrx7dYc2QN9bqeWfGzuGPkHSQEJXSsw7Ic+PhX0GcMXPxwp2Krrqvnu6MFLJgQ67Lr289kMimmDI7g8/05mOstuLt1Ysb00icgbQusvQfu/g58zy0pDw0bygtTX+Bw0WHe3Psmb/34FstTlnPdoOu4NfHWpjr7wrlZ8wrqC2Q0u5zZcJ3ohk6UnuDxbx9n1ppZrDqyitn9Z/Px3I/584V/7nhit1iMRFJXBVe/aaze6ITvjxZQY7YwtYdMyTSaOjiS0mozuzI6eEJTIw8fuHoJVOQbxz86WGdmUMggnr34WdZetZZpsdN47+B7zFw9k6d+eIqs8qzOxSjszpqRe0tDpw69WpRSi4BFALGxsR3pQnRQSmEKy/Yt4/MTn+Ou3Llu8HX8PPHn9Pbv3fnO//d3OPolXPF3CB/Y6e42H8rFx8ONifE9axrgwkHhuJkUm1JyGR/Xyefee5RxgPWLP8LWN2DSXR3uKiE4gWcufIZ7Rt3Dsh+XsfrIalYdXsWs+FncPuJ2+gf371yswi6sSe6ZQPPdeqOB7I48mNZ6CbAEjA2yO9KHsJ7WmuRTybz141t8k/UNfh5+LExcyM3DbibcJ9w2D5L6JWx+GkZcD0m3d7o7rTWbUnI5f0AY3h6uvQTyTIHeHiT1C2FzSi4PzzyHg9itOe9+yNgKnz8KfUZD7KROdRcTGMMT5z3BXaPu4p3977D6yGo+TvuYqTFTuW34bW2f9yC6nDXTMtuBgUqpeKWUJzAfWGffsERn1Fvq+eLEF9y0/iZu23gbBwoOcN+Y+/j82s95YNwDtkvsRSdg9e3GWvYr/2Fs4txJqbnlZBZV9bgpmUaXDIkkJaeM7GIblAcwmWDu6xAUAytvhbJTne8TYyvAhyc8zMZrNnLXqLvYmbuTmzfczK0bbuWrjK+waDn05gzaTe5aazNwL7AROAis1FrvV0o9qZSaA6CUGq+UygSuA95QSu23Z9CiZVXmKlakrODKtVfywJYHKKwu5LGJj7Hxmo0sGrmoza3szlltJay8BSz1cMO/wdM2q1o2pRhLIHvK+vYzNS79bPw7dJpPsPH/U10CHywEc61t+sXYIeqXo3/J59d8zsPjHya7Ipt7N93L3I/msvrwailS5mDKUUX9k5KSdHJyskMe29XkVOSwImUFHxz+gNLaUkaGj+TWxFuZFjvNqM5oa5Z6I7GnfArzl8OQWTbpVmvNZS98ja+nGx/de4FN+uxutNZMf+FrArzd+fCe823X8d4PYM0dMPIGmPeGTb5lnanOUsfnxz/nnf3vcLDwIKHeoVw/+HpuGHyD7b4tCpRSO7TWSe21k8Jh3ZTWmt15u1l+cDn/PfFfNJppsdO4aehNjIkcY78lhFobJyqlfAIz/2qzxA6w/XgRR3LL+ds1I23WZ3ejlOLGCbE8+ckB9meXkGirujojr4Oi47D5KeMs1mkdK8HcFg+TB1ckXMGs+Flsy9nGvw/8mzf2vMHSfUu5PO5ybhx6I8PDh9v8cUXLJLl3M1XmKj479hn/SfkPBwsPEuARwI1Db+TGITcSHdCJk1+s9d3LsG0JTL63UyswWvLe1hMEeLsze5QNVvB0Y9eMjeavn6WwfGs6T89rp47PubjoIShJN1Y3BcVA0s9t13czSikm9p7IxN4TOVF6gvcOvsdHqR/xcdrHjAwfyfwh87ks7jK83Lzs8vjCINMy3URacRofHP6Aj45+RFltGQOCB7BgyAJmJ8zuupKtO942TlQaNheu/b9z3jKvLQXlNUx+ZhM3TozliTmJNuu3u3rogz1s2HeSrY9eir+XDcdg9Wb4z3xj6erVb8KIrqkWUl5bzkdHP2JFygqOlx4n2CuYuQPmct2g64gNlGXR50KmZVxAlbmKz49/zpoja9iZuxN3kzvTY6dz/eDrGRc1rmvP3kz+P+OEmAHTjTlbGyZ2gFU7Mqmtt3DjRHmjA/xsYiyrdmTy0e4sfjaxn+06dnOH69+B966HNXca02wjr7Nd/63w9/TnZ0N/xoIhC9h6cisfHP6Adw+8y9v732ZCrwlcM/AapvWbJqN5G5KRu5PRWrMnbw8fHf2Iz459RnldOf0C+3H1wKuZ03+OYw5MbV8Gnz4IAy8zVl642/YNaLFopv59C1EB3qy8a7JN++6utNZc8dI3aGD9/RfY/oO8tgKW3wAnvoW5/4RRN9i2fyvkVuayNnUta46sIas8i0DPQC6Pv5y5A+aSGJbYY0pPnCsZuXczGaUZfHLsE9anred46XF83H24NPZS5g2cR1JUkmNe6Fob87Ob/gQDZ8AN79o8sQN8ezSfEwWVPHDpIJv33V0ppbhxYiyPrf2R3RnFjIm18W5Unn5w40pYfj18+AuoKrL5MZT2RPpGsmjkIu4YcQc/nPyBtalrWZu6lvcPvU//oP7M7j+bWfGz6OPfp0vjchUycnegUxWn+O+J/7Lh+Ab25u0FICkqiTn953BZ3GX4eTiwIqK51piG2f0ejLjOKOFrh8SuteamZVs5kF3K949M63FnpbalvMbMxKe/4PwB4Sy5pd2BWsfUVhrTMymfwIRFMOMZY+rGQUprS9l4fCPrUtexO283AGMjxzIzfibT+02XJZVYP3KX5N7Fcipy+DL9Sz4//jm7cneh0QwKGdS0hKyXXy9HhwiVhcY69uP/Myo8TnnELuuiATbsO8nd7+3kiSuHsfD8eLs8Rnf2yqYjPPf5Yf512wQuGnTum4xbxVIP/30cvn/F+IZ2zZvg7fitDTPLMll/bD3r09ZztOQoJmVifNR4Lu13KZfEXtJjq1NKcncSWmuOFB9hS8YWtmRsYV/+PgAGBA/gsrjLmBk3k/ggJ0pqx/4HaxZBRZ6xL+foBXZ7qKraeqb9fQuBPh58ct8FnStz66Kq6+qZ8Y+vcTMpPvvVRXi62/FvtH0ZrP+tsQ7+2rcg2k7fFjrgSNERNh7fyMbjGzleehyAURGjmBozlakxU4kPiu8xc/SS3B2osq6SbTnb+CbrG77J+qapPOqI8BFMi53GtNhpxAXFOTbIM9Wb4au/wtfPQmiC8ebuY99CUH///BAvb0rl/UWTmJgQZtfH6s42p+Ty87e388jlQ/jFxXauwJixDVbdDmXZMPVROP9XHd7g3B601qSVpPHFiS/4Mv1LDhYeBCAmIIYL+17I+X3PZ3yv8fi4+zg4UvuR5N6F6i31HCg4wA8nf+CHkz+wK3cXdZY6fNx9mNh7IlOip3BR9EVE+Nrpa3VnZWyDTx6EU/tg1I0w62/gFWDXhzyeX8FlL3zN5SN68eL8MXZ9LFdwxzvb+f5oAV/+Zgq9gjq+faFVqoqN8xkOrIW+4+CK5+3+Qd9RORU5fJ35NVsytrA9ZzvV9dV4mjwZGzWWSb0nMbnPZIaEDsGkXOdboSR3O6qrr+Ng4UF2ntrJ9lPb2XlqJ+V1xq7xg0MGM6n3JC6IvoCxkWPxdPN0cLRtqCiATU8aJycF9IHL/wLDrrL7w1bX1XPLsm3szy5h00NTiAq0c7JyAScKKpj+wtdMTghj6a1JeNh7Cktr2PcBbPw9VBYYB1unLAYfG6/asaFqczU7Tu3gm6xv+OHkD6QWpwIQ4BnAuKhxjI8az7iocQwOHYy7qfsuFJTkbkO5lbnsy9vHvvx97M7bzY/5PzZVvIsLjGN8r/GM7zWeCb0mEObTDaYXKguNg2db3zB2T5p0t/HGtfNoHaDeovnlezv5bH8O/7hhNHPHyKZe1npv6wke/fBHrhkbzXPXjeyaOeaqIvjyT5D8FngFwuRfGq8XbxtWGLWTvMo8tuZsJTknme0520kvSwfAx92HEeEjGBUxihHhIxgRMaJbrcKR5N4BWmtOVpzkcNFhDhYc5EDhAQ4UHCC30ii/6q7cGRI6hNGRoxkbNZYxkWO61YuCohOQvMw427SmFBLnGSthIgZ3ycNrrXl07Y8s35rOH2YP4/YLnOhAcjfx4hdHeOGLw/ziogQemTW06x44Zx9sfgYOfWqM3sffAeN+DkHd58P5VMUpduXtYtepXezK3cXhosPU63rAqFE/LHQYw8KGMTRsKINCBhHlG+WUB2klubdBa01eVR7HS46TWpzK0eKjpBancqT4CGW1ZQAoFPFB8QwNG0piWCIjwkcwNGxo9zs92lxj7Ja0819w+DNjSeOQ2cYSx15dV6Gvrt7C3z5L4c3/HePuKf1ts9NQD6S15o/r9vOv709w/7SB/GraQNxMXZiAsnfBV3+DQxtAmWDIFTDmZug/tdN753a1KnMVBwsOsi9/H/sL9nOw4GDTShyAIK8gBgYPpH9wfwYED6B/cH/ig+IJ8w5zaNLv8cm93lLPqcpTZJVnkVWeRXppOhllGaSXpXOi9AQVdRVNbQM8Augf3J+BIQMZHDKYwaGDGRQyqOsKctladamxRv3gJ0bN9ZoS8IuAsbcalQCDuqB6ZDNHTpXxmw/2sDezhJsn9ePJq+TU8s6ot2h+u2oPa3ZmMT4uhOeuG0W/sC4+4a3ouLF0cte7xtSNTwgMvdIYOPQ7H7z8uzYeGymvLedw0WEOFR3iUOEhjhQf4Wjx0dPyhb+HP3GBccQExhAbEEtMQAx9/fsSHRBNhE+EffZQaMamyV0pNRN4EXADlmqt/3LG7V7Av4BxQAFwg9b6eFt9dia5V9ZVUlBVQH51PnmVeeRW5pJbmcupylPkVOSQU5FDbmUuZm1uuo+bcqOPfx9iAmKIC4wjLiiOuMA4+gf3J8Inonsnm4oCyEqGzGQjqWdsA10PXkEwdDYkXg0JF3f5yKqgvIblW9N5eXMq/l7uPDV3OLNG9OxyvraitWbt7iwe/2g/5nrNry8dyPzxsQT5dvHo2VwDRzfBj2vg0HqoLQeTh7Ffa9wF0DcJ+o4F3+672bnWmlOVp0grTuNY6TGOlxzneOlxMsoyOFlx8rRtBd1N7kT5RtHLrxe9/HoR6RtJlG8Ukb6RRPhEEOYTRoRPBN7uHV9EYLPkrpRyAw4D0zE2y94OLNBaH2jW5h5gpNb6LqXUfGCe1rrNSkQdTe5L9y3lxZ0vnnW9h8mDSN9Ievn1ordfb3r59aKPfx/jE9U/mt7+vfEwda+vjaexWKDspDFiKjoO+YcgNwXyDkKxcaAIZYJeI2HANOh/CURPAPeuXa1TWWsm+XgRq3Zk8tmPOdTWW5iRGMVTc0cQEdDNprS6gZMlVTyyZh9bDuXh5W5i9sg+XDO2L2NiQ/Dx7OL16XXVkPGDkeyPboKcH4GG/BISBxFDjf12wwcZl0PiwD/K5hVGu1JdfR1Z5Vlkl2eTWZ5JVnlW0wAzpyKH3KpczBbzWfd7dOKjzB8yv0OPacvkPhl4Qms9o+HyIwBa62eatdnY0OZ7pZQ7kANE6DY672hy35O3h+ScZMJ9wpt+In0jCfYKds7Rt9ZgMUN9rTHKqa8Fc7Xxe20F1FUa9T1qSo2f6lKoKjRWtFQWQnmOsbFxeY7RTyOTh/EmiRxiJPToJOg92u5fh+vqLZRW1VFabaa4spaTJdVkFlWSXljJnowSDpwspd6iCfB255qx0dw4MZZBUfZfhdPT7c8uYfnWdNbuyqKith53kyKxbxCjooOIDfWlb7APvYN9CPLxIMjHg0Bvd/ufEVxdaszRZyUbB2RzU6DgyOmvYzdPI8EH9DL+9Q0Fn1DjX69AYwWXdxB4+IKHj1HwzN0L3L2Nf908jR+Tu91KZHSGRVsoqi4itzKXguoC8qvyya/K57w+5zEsbFiH+rRlVci+QEazy5nAxNbaaK3NSqkSIAzIty5c69X+bwuX/vjmadeVNvxYQ9H880Y3u/7sNgoNWjfdZlyvMaFRDT/G7xZMWDBpC26Nv2PBjXrcqT/HZwi1uFOmAilVARSqEApMgyhwn8gpUxQ5pihyVBQ5pkjqq90hHeNnWz2w47R+Wvtkbf6Zq5s11IBFa+PHYsztmi2aeouFGrPxU29puddAb3cS+wRx98X9GRcXwqT4sK4fOfZgiX2CeHreCB6ZNZStaQUknyhix4kiPtyZRVnN2SNHAHeTwsvdhKe7CXc3E+4mhUkpTCaMf5X66X2hzniPtJJIW742qeEH3P3qiLLk0lvn0MtyiihLHqGVhYSVFxKq9xGoywjUpXjQcsxtMeNGfbN3YD0mLMr4XWPC0vSuVVhQ0HSZpg+Gxne7bvZMTn/FN7/e+g8T34afmIbL+eOAKzqW3K1lTXJv6Rmc+Q63pg1KqUXAIoDY2I5tyuAeEE6+b0KH7tsskqbf2vtP1KrxRfDT9RZMTdc3vnC0akjxykjrFuVmpHflRr1yx6zcqcedOpMXdcoTs/KkRnlTa/Ki1uRDtcmXKpMfVSY/apV3m6MQX8Dav4Bq7QWoTv+18c3qpow3Nsp487uZTE1JwNvDDS93EwHe7gT5ehDo7UHvIB/6hhgjQuF4/l7uTBsaxbShUU3XlVTWkVFUSU5JNaXVdZRW1VFWbabaXE9NnfGh3fghbrZo0MaHfH3jh77Wp783Whk16FaHE2cKoYTBlACHWuxI46Wr8baU42OpxNtSiaelCi9LNZ66Gnddh4euxcNSgxtm3LUZN23GTdcbKb3pXyPNK/3TAAw0Suuffm/2hFTToKftQV+bfwQrefrb/xiENck9k58+cACigexW2mQ2TEHq1jwAAAOdSURBVMsEAYVndqS1XgIsAWNapiMBj5n+M5j+s47cVYgeKcjXgyDfIIb3dXylR9F1rJl02w4MVErFK6U8gfnAujParANubfj9WmBTW/PtQggh7KvdkXvDHPq9wEaMpZBvaa33K6WeBJK11uuAZcC7SqlUjBF7xw4DCyGEsAmrqudordcD68+47vFmv1cD9t9lVwghhFW67wJTIYQQrZLkLoQQLkiSuxBCuCBJ7kII4YIkuQshhAtyWMlfpVQecMIhD9454dihrIKT62nPuac9X5Dn3J3001q3uyGzw5J7d6WUSramaI8r6WnPuac9X5Dn7IpkWkYIIVyQJHchhHBBktzP3RJHB+AAPe0597TnC/KcXY7MuQshhAuSkbsQQrggSe6doJR6SCmllVLhjo7FnpRSzyqlUpRSe5VSHyqlgh0dk70opWYqpQ4ppVKVUosdHY+9KaVilFKblVIHlVL7lVK/cnRMXUUp5aaU2qWU+sTRsdiDJPcOUv+/vft5sTEMoDj+PUVZYK1QLAmlNKlZkJH8mMaaSNlamCKF/wELysJGmZKirJTxB7AwzSw0G0lqIsqCneRYvO/dzehm5n2f5pnzWd3uvYvzduv03B/dI22nGQ3/VDpLD6aBPbb30YylXy+cpxPtGPw94ASwGzgjqdsttPJ+A1ds7wIOApfWwDUPXAbmS4foSsr9/90GrrHcva1VwPZL24NRy9c0a1w1GgHe2/5g+xfwGDhdOFOnbH+2PdPe/klTdlvLpuqepG3AKeBB6SxdSbn/B0kTwILtudJZCrgIvCgdoiOLjcFXX3QDknYA+4E3ZZP04g7N4exP6SBdGWqsYy2S9ArYsshDN4EbwLF+E3XrX9dr+3n7nJs0b+On+szWo6GG3mskaSPwFJi0/aN0ni5JGge+2n4r6XDpPF1JuS/B9tHF7pe0F9gJzEmC5iOKGUkjtr/0GHFFLXW9A5IuAOPAWMX7uMOMwVdH0nqaYp+y/ax0nh6MAhOSTgIbgM2SHtk+VzjXisrv3JdJ0kfggO3V+AdEQ5F0HLgFHLL9rXSerkhaR/OF8RiwQDMOf9b2u6LBOqTmhPIQ+G57snSevrUn96u2x0tnWWn5zD2GcRfYBExLmpV0v3SgLrRfGg/G4OeBJzUXe2sUOA8caV/b2fZEG6tcTu4RERXKyT0iokIp94iICqXcIyIqlHKPiKhQyj0iokIp94iICqXcIyIqlHKPiKjQXxc7zFOj4jTtAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1635f4ea2b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "''' 观察正态分布下，不同sigma值对幅度的影响 '''\n",
    "\n",
    "%matplotlib inline\n",
    "import scipy.stats as sps\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x = np.linspace(-5, 5, 100)\n",
    "mu = 0\n",
    "for sigma in [0.5, 1.0, 2.0]:\n",
    "    y = sps.norm.pdf(x, mu, sigma)\n",
    "    plt.plot(x, y)\n",
    "    \n",
    "labels = ['sigma=0.2', 'sigma=1.0', 'sigma=5.0']\n",
    "plt.legend(labels)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1636228c978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "''' 观察正态分布下，不同mu值对中心线位置的影响 '''\n",
    "\n",
    "%matplotlib inline\n",
    "import scipy.stats as sps\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x = np.linspace(-5, 5, 100)\n",
    "sigma = 1.0\n",
    "for mu in [-2.0, 0, 2.0]:\n",
    "    y = sps.norm.pdf(x, mu, sigma)\n",
    "    plt.plot(x, y)\n",
    "    \n",
    "labels = ['mu=-2', 'mu=1.0', 'mu=2.0']\n",
    "plt.legend(labels)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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DOsKd34FvcN3rtBOjxch3x7/jg5gPyCrN4poO1/DQgIfoGmSnDzVRIw03uTtJQ53y1xY1mRZY1I9Pd5zGw83A/VfZYbx59kn47P/Aqznc+W2DSuzbkrfxWtRrnMo7xaCWg1g4biH9Q/s7O6wmreEm92pa2I7SUKf8tUVISAi5ubmYTCbc3d0vOy2wcLzichOr9iUzqW9rgpvV8SackhxrYreYrF0xAeH2CbKOEvITeCPqDTYmbaS9f3sWjl3ImHZjpFHRADTc5O4kDXXKX1sopRg7dizffPMNU6dOZdmyZdx00011rlfUzn9/P0NBmYk/Davj7IsWM/znXshNhOn/hdDu9gmwDsrN5Sw5uITF+xfjbnBn9uDZTOs1Te4kbUAkuVfSUKf8TU1NJTIykvz8fAwGA++88w6xsbE0b96cSZMmsXjxYsLCwnjttdeYOnUqf/vb3xg4cCAzZsyo8c9A2MfnuxPo2tKPIR2D6lbR+vkQtw5ueAfaD7dPcHUQlRrFSzteIj4/ngkdJ/DUkKdo6WvnqRREncmUvzUkU/4KWxxKyeP6hVuZd0Nv7rmyU+0rOvgtfPNn6+Rfk9+xX4C1UFheyJt73uSbY98Q7hfO34b/jZFtbW+gCPuQKX8dRKb8Fbb4YlcCXu4G/m9QHfrGs07A97Og3TCY+Lr9gquFbcnbeGHHC6QXpzO9z3QeinhIbj5q4CS515BM+SuqU1Rm4vuYFK7v34YA31pO3mUqh//MsE7+NeUTcHdOX3axsZg3o99k5bGVdA7ozPKJy2UUTCMhyV0IO1tz4AyFZSbuGFaHFY82/gNS9sEfl0NAW/sFVwMHMg7wzNZnSMhPYHqf6cwaOKvJrD/qCiS5C2FnPx1MpW2gD4Pa1/JC6qnNsPUdGHQ39L7RvsHZwKItfHzwY97b9x6hvqEsuW4JQ1oPqfc4RN1IchfCjgrLTGw5nsmdIzrUbqx3aR589wC06AoTXrF/gNXILMnk2a3Psj1lO9d2uJbnr3i+SS8y3ZhJchfCjtYfSafcbGFC39a1q2DdC1BwBu5dB571u1hFVGoUf9n8FwrKC5g3Yh5Tuk2Rm5EaMZk4zAYNYcrfjRs3EhAQQEREBBEREbz00ktVlpMpf53r54OphPh51a5LJn4bRH8Mwx+q18WstdYsPbiU+365Dz8PP764/gtu7X6rJPZGTpK7DRYvXkzv3r2dHQajRo0iJiaGmJgY5s2bV2WZc1P+Hj9+nKCgIJYsWVLPUTZdpUYzG46mc12fVrgZapgYjaXww6MQ2MG6RF49KTIW8cTGJ3hzz5uMaz+OL6//ku5Bzr8DVtSdJPdKGuqUv7aQKX+da/OxDIrLzbXrktn8OmTFweR36607JjE/kTt+vIMNiRuYEzmHN0e/iZ+nX72cWzheg+1zf233axzJPmLXOnsG92Tu0LmXLdOQp/zdsWMHAwYMICwsjAULFtCnT58LysqUv87106FUmnu7M7xzi5odmH4Etr0LEXdAl7GOCa6SnWd28uTGJ1FK8eE1HzK8jfOnNRD21WCTu7M01Cl/Bw0axOnTp/Hz82PNmjXcfPPNHD9+/IIyMuWv8xjNFtbFpnF171Z4uNXgC7HW8NNca2v9mvmOC7CCFUdW8MruV+gU0ImFYxfSrnm7ejmvqF8NNrlX18J2lIY65W/z5v8bjjZp0iQeeughMjMzCQkJOb9dpvx1nh0nssgvNTGhTw27ZI78aF0LdeLr0KyGLf4aMlvMLIhewGeHP2N0+Gheu+o1mnnU74gcUX9sSu5KqQnAu4AbsFhr/Wql/e2BZUDg2TJPa63X2DnWetFQp/xNTU2lVatWKKXYvXs3FouFFi0uTAYy5a/zbDiajpe7gau6h9p+kLEUfv4rhPaCSMfO3llsLGbulrlsTNzIHb3u4KnIp3AzuDn0nMK5qk3uSik34H3gGiAJiFJKrdZaVxwb+DdgpdZ6kVKqN7AG6OiAeB2uoU75+80337Bo0SLc3d3x8fHhq6++Ot/lIlP+Ot/W45kM7RSMt0cNEuaO9yD3NNz1Pbg57kt0VkkWD//2MIezD/PM0Gf4U68/OexcogHRWl/2AYwAfq7w+hngmUpl/gXMrVB+e3X1Dh48WFcWGxt70baGpqCgQGuttdFo1DfccIP+9ttvnRxR7TSGn3VjkZpXojvM/a/+cGOc7QflpWj999Zaf3WH4wLTWifkJ+hJ/5mkI5dH6vWn1zv0XKJ+ANG6mvyqtbapW6YtkFjhdRIwrFKZF4BflFKPAM2Aq2v7YdPQyZS/orKtxzMBGNk1pJqSFWx6FcxGh15Ejc2K5cF1D2LWZv597b+JaBnhsHOJhseW5F7VcIvKVxZvB5Zqrd9USo0Aliul+mqtLRdUpNRMYCZA+/Z1mDHPiWTKX1HZtrhMgpt50ruNjXOwZMbB3uUw5F4IrsNCHpcRnRrNI+sfwd/Tnw+v+ZDOAZ0dch7RcNkyZisJqDhWKhxIqVRmBrASQGu9A/AGLmrGaK0/0lpHaq0jQ0OrvvCknbQyVFMiP2P70VqzNS6TK7q0wGDrXanr54OHD1z1lENi2py0mQfWPUCobyifTvxUEnsTZUtyjwK6KaU6KaU8ganA6kplEoDxAEqpXliTe0ZNg/H29iYrK0uSjwNprcnKysLb29vZobiE4+mFpBeUMaqbjV0yyXshdhWMmAV+NRhZY6Of4n/isfWP0TmgM0snLKV1s1pOYCYavWq7ZbTWJqXULOBnrMMcP9ZaH1JKvYS1Y3818CTwb6XUbKxdNtN1LTJ0eHg4SUlJZGTU+HNB1IC3tzfh4XVY/k2ct6Wm/e3rXgDfELhilt1jWX1iNc9te46I0AjeG/8e/p7+dj+HaDxsGn+lrWPW11TaNq/C81igzivlenh40KmTY/oghXCEbXGZdAppRniQb/WFT26CU5tgwmvgZd/E++3xb3lh+wsMbT2UheMW4uthQzzCpcnEYULUUrnJws6TWYzsasOdpVrDxlfBPwwi/2zXOFYcWcHz25/nirZX8N749ySxC0CSuxC1FpOYS3G5mSu72tB3Hr8FErbDlbPB3X7rkK48upK/7/o7Y8LHsHDsQrzd5VqKsGqwc8sI0dBti8vEoGCELbNAbnwN/NvAoLvsdv6vj33N/J3zGR0+mrfGvIWHm4fd6haNn7TchailqPhserVpToBvNUk1fiuc3gojHwcP+7Ssvz3+LS/teIlRbUdJYhdVkuQuRC0YzRZiEnOJ7GDDcnobXwW/VjD4bruc+4cTP/DC9hcY2XYkb499G083T7vUK1yLJHchauHwmXyKy81Edgy+fMHTO6z97SMft964VEfrTq/juW3PMbT1UN4Z8w5ebvbrvxeuRZK7ELUQHZ8DQGTHalru294B3xYweHqdz7k5aTNPbX6KfiH9WDhOLp6Ky5PkLkQt7DmdQ9tAH9oEXKY1nhYLx36CofeDZ92GJ0anRvPExifoFtiND67+QIY7impJcheihrTWRMVnV99q374QPHxh6H11Ot/hrMM8sv4RwvzC+Nc1/5I7T4VNJLkLUUNJOSWkF5Rd/mJqbiIc+BoG3Q2+1fTLX0Z8XjwPrHsAf09/PrrmI4K8bbiAKwSS3IWosaj4bIDLX0zduch6V+qIh2p9nvTidO7/9X4APrrmI5kETNSI3MQkRA1Fn87B38ud7q0u0T1SnA17lkK/KRBYu3UL8svzeWDdA+SW5fLxhI/pGNCx1vGKpkmSuxA1FB2fzaAOQbhdav72PZ+AsQiueLRW9ZeZy3h0/aOcyjvFB+M/oE+LPnWIVjRV0i0jRA3kFRs5llZ46f52sxF2/xs6j4XWfWtcv9li5pktz7AnbQ//uPIfjAgbUceIRVMlyV2IGtibcG58+yX622O/h4IzMLx2fe0Lohfw6+lfeSryKSZ2mljbMIWQ5C5ETUTFZ+NuUES0C7x4p9aw431o0RW61nyN+OWxy/ns8GdM6zWNu/rYb4Ix0TRJcheiBmISc+nZxh8fT7eLdybuhpS9MOwBMNTsT+vX07/yRtQbXN3+auZEzrFTtKIpk+QuhI0sFs2BpLyqW+0AOz8A7wCI+FON6v0943ee2fIM/UP788qoV3AzVPHBIUQNSXIXwkYnM4soKDPRP7yK5J6bAIdXW+eQ8Wxmc51JBUk8uv5RWvq2lPlihF1JchfCRr8n5gJU3XKPWgwoGGL7VAP55fk8/NvDmCwm3h//PsHetb+TVYjKZJy7EDban5RLM083uoT6XbjDWAp7l0PPSRDYzqa6jBYjT258koSCBD665iM6BcjC8MK+JLkLYaOYpDz6hQdcfPPSoW+hJNvmVrvWmld2vcLOMzuZP3I+Q1oPcUC0oqmTbhkhbFBusnA4JZ8BVfW37/4IQnpAp6tsquuLI1/w9bGvmdF3Bjd3vdnOkQphJcldCBscSc2n3GxhQOX+9qQ9kLLPOq2vusR0BBVsTd7K61GvM67dOB4dVLvpCYSwhSR3IWxw7mLqRck96t/g6Qf9b6u2jpO5J3lq01N0D+rOK6NewaDkz084jvx2CWGDmMQ8Qvw8CQuoMFSxKBMOfgsDpoJ388sen1eWx6z1s/By8+Kf4/4pKykJh5MLqkLY4PekXAaEB6Iqdr3sWw7msmovpJosJp7c9CSpRal8fN3HMi+7qBfScheiGgWlRk5kFF7YJWOxWOds73AltOx52ePfiHqDXWd28fyI54loGeHYYIU4S5K7ENU4kJyH1pX6209ugJx4iPzzZY/99vi3fHHkC+7ufTc3db3JsYEKUYEkdyGq8XtiHgD92wb8b2P0x+DbAnpNvuRxMekxzN85nyvCrmD24NmODlOIC0hyF6Ia+5NyaR/sS1AzT+uG/DNwdC0MnAbuXlUek1aUxuyNs2nTrA2vX/W6TAYm6p1NyV0pNUEpdVQpFaeUevoSZf6olIpVSh1SSn1h3zCFcJ4DydY7U8/btxy0GQbdXWX5MnMZszfOpthYzMKxCwnwCqiynBCOVO1oGaWUG/A+cA2QBEQppVZrrWMrlOkGPAOM1FrnKKVaOipgIepTbnE5STklTBvewbrBYoY9y6zL6LXoclF5rTV/3/l3DmQe4J0x79A1qGs9RyyElS0t96FAnNb6pNa6HPgKqHxl6D7gfa11DoDWOt2+YQrhHAeT8wHoG3a29X38V8hPuuSF1JVHV7IqbhX397+f8R3G11eYQlzEluTeFkis8Drp7LaKugPdlVLblFI7lVITqqpIKTVTKRWtlIrOyMioXcRC1KODKdaLqX3Czt6ktOcT8GsFPSZdVHZv2l5e3f0qo9qO4qGI2q2hKoS92JLcq5owQ1d67Q50A8YAtwOLlVIXzbCktf5Iax2ptY4MDQ2taaxC1LuDyXmEB/lYL6bmJcPxXyDiDnDzuKBcWlEaT2x8gjC/MF696lWZWkA4nS2/gUlAxUmqw4GUKsp8r7U2aq1PAUexJnshGrWDyXn/65KJ+Ry0BQbdeUGZcnM5T2x6gmJTMe+OfZfmnpefikCI+mBLco8CuimlOimlPIGpwOpKZVYBYwGUUiFYu2lO2jNQIepbfqmR+Kxi60gZi8W6IEenqyC48wXlXo96nf0Z+5k/cr5cQBUNRrXJXWttAmYBPwOHgZVa60NKqZeUUjeeLfYzkKWUigU2AE9prbMcFbQQ9eHQ2YupfcKaW+9IzUu4aPjjqrhVrDi6gj/3+TPXdbzOGWEKUSWbJg7TWq8B1lTaNq/Ccw08cfYhhEs4dPZiat+2AbBmGfgEX3BHamxWLPN3zGdY62EyN7tocOSqjxCXcCA5jzYB3oSQD0fWwIDbz9+RmluayxMbnyDYJ5jXR7+Ou0EmWBUNi/xGCnEJB5Pz6BMWAL9/ARYjDLZ2yZgtZp7e8jTpxeksm7CMYO9gJ0cqxMWk5S5EFQrLTJzMLKJfWHPY+ym0Gw6hPQD4cP+HbEvZxjPDnqFfaD8nRypE1SS5C1GFw2fy0RpGeh2HrDgYdBcAm5M28+HvH3Jz15uZ0m2Kk6MU4tIkuQtRhQNJZ+9MTf0ePP2hz80kFiTy9Jan6Rnck2eHPXvhqkxCNDCS3IWowsGUPDr6mfE5/gP0/QOlBjee2GgdDPbWmLfwdveupgZ4WFFiAAAdMklEQVQhnEsuqApRhUPJ+Uxvvgeyi9ED7+LlXS9zJPsI749/n3b+7aqvQAgnk5a7EJWUGs3EZRRyXfkv0LI335bEsypuFTP7z+Sq8KucHZ4QNpHkLkQlR1IL6KpP06YwlkO9JvCPXa8wos0IHhogMz2KxkOSuxCVHEzO4za3jeS6e/Fk5laCfYJ57arXZKk80ahIcheikiNJmdzsvpW/duhGWmkmb45+kyDvIGeHJUSNSHIXohL/07/wdaCBLZZ85g6ZS//Q/s4OSYgak+QuRAVGs4Wg8u95PzCASR0ncluP25wdkhC1IsldiAqiY7fyWat8wg3+PH/FC3Kjkmi0JLkLcZbRbOT1fc9SrhR/jZiPr4evs0MSotYkuQtx1oKoN4jTudyR4ceIvuOdHY4QdSLJXQhgzck1fHH0S+7My6fc/SbcDNIdIxo3Se6iyYvLieOFHS8w0ODHjCwjRZ1kuTzR+ElyF01akbGI2Rtn4+PmzRsJJ1ltvpIe4aHODkuIOpPkLposrTXzts0joSCBBS1H08pYykrzGOvqS0I0cpLcRZO1PHY5v5z+hUcHPsqQo+s506wncYaOdG/l7+zQhKgzSe6iSdqTtoe39rzFuHbjuCcoAtIO8pPntXRv5Y+nu/xZiMZPfotFk5NZkslTm56irV9b/n7l31H7lqPdffg4dxB9wpo7Ozwh7EKSu2hSjBYjczbNoaC8gLfGvIU/Bjj4H0q6XU9iiSf92kp/u3ANktxFk/LunnfZk7aHeSPm0SO4B8R+D2X5HGh5MwB9JbkLFyHJXTQZP8f/zLLYZUztMZXJXSZbN+5dDsFd2FreDTeDolcb6ZYRrkGSu2gSTuae5Lltz9E/tD9/GfIX68bM45CwHQZO40BKPt1a+uHtIQtyCNcgyV24vMLyQh7f+Dg+7j68OfpNPNw8rDv2LgODOzriTxxMzpPx7cKluDs7ACEcSWvNc9ueIyE/gX9f+29aN2tt3WEqh5gvofsE0iyBZBaW06+tdMkI1yEtd+HSPj74MesS1jF78GyGtB7yvx1Hf4TiTBg8nYPJeYBcTBWuxabkrpSaoJQ6qpSKU0o9fZlyU5RSWikVab8Qhaid7SnbWbhvIRM6TuCu3ndduHPPMghoB13GcSA5D4OC3jLGXbiQapO7UsoNeB+YCPQGbldK9a6inD/wKLDL3kEKUVPJhcnM3TyXzgGdefGKFy9cUSknHk5ugIHTwODGoZQ8uoT64espvZTCddjSch8KxGmtT2qty4GvgJuqKDcfeB0otWN8QtRYiamExzc8jtli5p2x71y8otK+z0AZrMkdOJCcJ10ywuXYktzbAokVXied3XaeUmog0E5r/V87xiZEjWmteXHHixzNPsqrV71Kh+YdLixgNlmTe9erISCc9IJS0vLLJLkLl2NLcq9qSRp9fqdSBuBt4MlqK1JqplIqWikVnZGRYXuUQtjo88Of8+PJH3k44mGuCr/q4gLHf4aCMzB4OgCHkvMB6Cv97cLF2JLck4B2FV6HAykVXvsDfYGNSql4YDiwuqqLqlrrj7TWkVrryNBQWRBB2NfuM7tZEL2Ace3GcV//+6ouFP0x+IdBN+tqS+dGyvSRlrtwMbYk9yigm1Kqk1LKE5gKrD63U2udp7UO0Vp31Fp3BHYCN2qtox0SsRBVSC5M5slNT9KheQdevvJlDKqKX+2ceIj7DQbdBW7Wi6cHkvPoHNIMPy+5mCpcS7XJXWttAmYBPwOHgZVa60NKqZeUUjc6OkAhqlNsLOax9Y9htph5d+y7+Hn6VV1wzzJQyprczzqYnCetduGSbGquaK3XAGsqbZt3ibJj6h6WELbRWvP89uc5lnOMD67+gI4BHasuaCqHfcuh+wQIsI4HSC8oJSWvlHvCJbkL1yN3qIpGbcnBJfwU/xOPDXqMK9teeemCR3+EogwY/Ofzm/YnWvvbB7QLdHSYQtQ7Se6i0dqQsIGFexcysdNE7ul7z+ULR38MAe2h6/jzm/Yn5eJmULL6knBJktxFo3Q85zhPb3maXi168dIVL114B2plmcfh1GYYfBcY/jelb0xSHt1b+cudqcIlSXIXjU5uaS6PrH8EXw9fFo5diLe79+UPiFoMBg8YdPf5TVpr9iflEtFO+tuFa5Imi2hUjGYjj298nIziDD6Z8AmtmrW6/AFlhRDzBfS5Gfxant+ckF1MbrGR/uHS3y5ckyR30WhorZm/cz570vbwyqhX6B/av/qD9q+AsnwYcuFNTTGJuQAMkOQuXJR0y4hG49PYT/ku7jtm9p/JDZ1vqP4Ara1dMq37Q7uhF+z6PTEPbw8D3VtdYky8EI2cJHfRKGxM3Mib0W9yTYdreDjiYdsOOr0d0mNh6H3Wm5cq2J+US9+wANzd5E9AuCb5zRYN3uGsw/xl81/o3aL3pacWqMruj8A7EPpOuWCz0WzhYEqejG8XLk2Su2jQ0orSmPXbLAK8AvjnuH/i4+5j24H5KXDkv9Y52z0vnM/9WFoBpUaLJHfh0uSCqmiwio3FPLL+EYpMRXw68VNCfWswk2jUYtAWGHLvRbv2J529M1WmHRAuTJK7aJBMFhNzNs3hWM4x3hv/Ht2Dutt+cHkxRH8CPSZBcKeLdv+emEugrwftg32rOFgI1yDdMqLB0Vrz8q6X2ZK8hb8O++vl54ypyv4VUJINwx+qcndMYi4DwgMvf1erEI2cJHfR4Cw+sJhvjn3Dvf3u5Y89/lizg7WGnYuswx87XHHR7sIyE8fSCqS/Xbg8Se6iQfnhxA8s3LeQSZ0m8cjAR2pewYn1kHkURjx80fBHgJiEXCwaIjsE2SFaIRouSe6iwdiWvI152+YxpPUQ5o+cb/uQx4p2LgK/VtDnlip3R5/OxqBgYHtpuQvXJsldNAiHMg8xe+NsugR24d2x7+Lp5lnzSjKOQtyv1hEy7l5VFomOz6Fn6+b4e3vUMWIhGjZJ7sLpEvITeOi3hwj2DmbR1Yvw9/SvXUXbFoK7D0RWPbe7yWxhX0IOkR2lS0a4PknuwqnSi9OZ+etMtNZ8ePWHNRvLXlFesnWUzKA7oVlIlUWOpBZQVG4msmNwHSIWonGQce7CafLK8rj/1/vJKc3h4+s+vvT6p7bYtch609KIS887Ex2fDcjFVNE0SHIXTlFsLOahdQ+RkJ/AoqsX0SekT+0rK8mF6KXWi6hBHS9ZLOp0Dm0DfQgLtHEKAyEaMemWEfWuzFzGYxse42DWQV4f/TpD2wyt/qDLiV4C5QUw8rFLFtFaEx2fzWBptYsmQlruol4ZzUae3PgkO8/s5OUrX2Z8+/HVH3TZCkth54fQZTy0ufTiHUk5JaTll8nFVNFkSMtd1BuTxcTTW55mU9Imnhv+HDd2ubHule5bDkXpl221A+w5nQNAZAe5mCqaBknuol6YLWae3/48v5z+hTmRc2o+rUBVTGWw9W1oNxw6XXXZotGns/H3cqdH61oOsxSikZHkLhzOoi08v/15Vp9YzayIWdzd5277VLzvM8hPhjFzq5xqoKLo+BwGdgjCzSCThYmmQZK7cCiLtvDC9hf4/sT3PDTgIe4fcL99KjaVW1vt4UOh89jLFs0tLudoWoEMgRRNiiR34TAWbeGlHS/xXdx33N//fh6MeNB+lcd8DnmJNrXad5zIQmsY2bWF/c4vRAMno2WEQ5gtZuZtn8fqE6u5r999ti9qbQtTOWx5C9pGWkfJVGNLXCZ+Xu70D5fJwkTTIcld2J3RYuTZLc+yNn4tD0c8zAMDHrDvCWI+g7wEuOGtalvtANviMhneuQUebvJFVTQd8tsu7KrcXM5fNv2FtfFreXzQ4/ZP7OXFsPE16wiZrldXWzwxu5jTWcVcKV0yoomxKbkrpSYopY4qpeKUUk9Xsf8JpVSsUmq/Uuo3pVQH+4cqGrpzC1qvS1jH3CFzmdFvhv1PsmsRFKbCNS/a1GrfGpcJwJXdajkhmRCNVLXJXSnlBrwPTAR6A7crpXpXKrYPiNRa9we+AV63d6CiYTs3CdjOMzt56YqXmNZ7mv1PUpwNW9+F7hOh/XCbDtl6PJPWzb3pEtrM/vEI0YDZ0nIfCsRprU9qrcuBr4CbKhbQWm/QWheffbkTCLdvmKIhyyjO4J6f7+Fg1kEWjF7ALd2qXgWpzra+BWX5MH6eTcUtFs22E5lc2S1EFsMWTY4tyb0tkFjhddLZbZcyA1hb1Q6l1EylVLRSKjojI8P2KEWDdSrvFNPWTCOxIJH3x73PNR2uccyJ8pJh10cw4HZoVfmLY9UOpeSTW2zkyq5Vz+8uhCuzJblX1eTRVRZUahoQCbxR1X6t9Uda60itdWRoqPSBNna/Z/zOXWvvotRcyifXfcIVba9w3Ml+e9H679hnbD7kXH/7SEnuogmyJbknAe0qvA4HUioXUkpdDTwL3Ki1LrNPeKKh+u30b9z78734e/rz2cTP6jYfe3USdllXWbriEQhsb/NhW+My6Nnan1D/qtdTFcKV2ZLco4BuSqlOSilPYCqwumIBpdRA4F9YE3u6/cMUDYXWmqUHlzJ742y6B3Vn+cTltGvervoDa8tigbV/Af8wGPWEzYeVGs1ExedIl4xosqq9iUlrbVJKzQJ+BtyAj7XWh5RSLwHRWuvVWLth/ICvz164StBa22E+V9GQGC1G/rHrH3xz7Buu7XAtL1/5Mt7u3o49acxncCYG/rAYPG0f8bL5WAblJguje0j3n2iabLpDVWu9BlhTadu8Cs+rv5tENGo5pTk8uelJolKjmNF3Bo8OehSDcvA9cCW5sO5F6w1L/abU6NCfDqUS4OPB8M5y85JommT6AVGtYznHeHT9o2QUZ/CPK//B5C6T6+fEG16G4iyY9h+bblg6x2i2sC42jWt6t5YpB0STJcldXNZP8T8xb9s8/Dz8WDphKf1C+9XPiRN2we5/w9CZEBZRo0N3nMgiv9TEhL6tHRScEA2fJHdRJaPFyFvRb/HZ4c8YEDqAt8a8RUvflvVzclMZrH4EAsJh/HM1PvynQ6n4eroxqptcTBVNlyR3cZH04nSe2vQUe9P3ckevO3hy8JN4uHnUXwBb3oLMo3DHN+BVs2XxzBbNL4fSGNujJd4ebg4KUIiGT5K7uMCWpC08u/VZSs2lvDbqNSZ1nlS/AaQfhi1vQr8/Qrea3+26NyGHzMIy6ZIRTZ4kdwGA0Wxk4b6FLD20lO5B3Xlj9Bt0Duhcv0GYyuDbmeDdHCa8Uqsq1h5IxdPNwNie9dSFJEQDJcldcDL3JE9veZrD2Ye5rcdtzImc4/jx61VZPx9S98PUL6FZzfvLtdb8fCiVUd1C8POSX23RtMlfQBNm0Ra+PPIlb+95G193X94Z+w7j21e/bJ1DnNgA2/8JkfdAz9p1Be1LzCU5t4THru5m5+CEaHwkuTdRSQVJvLD9BXal7mJU21G8NPIlQnycNLqkKAu+ewBCesC1L9e6mi93JeDr6cZE6W8XQpJ7U2PRFlYcXcHbe97GoAzMGzGPKd2mOG++c4sZVj0AJdlwx9fg6VuravJKjPywP4VbBrbF37seR/YI0UBJcm9CjuccZ/7O+exL38fIsJE8P+J52vi1cW5QG/4Bx3+B69+ENv1rXc2qfcmUGi38aais8CgESHJvEkpMJXz4+4d8euhT/Dz9mD9yPjd1ucn5qxMdWgVbFsCguyGy9uutaq35YlcC/doG0C88wI4BCtF4SXJ3YVprfjn9CwuiF5BalMrNXW/micFPEOQd5OzQIO0QrHoIwofCpDdqNHdMZXsTcjiaVsArf6inqRGEaAQkubuoo9lHeXX3q0SnRdMjqAevjnqVwa0GOzssq7xk+OI2692nty0H97otpvH5rgT8vNy5cUCYnQIUovGT5O5iUotS+ee+f/LDiR8I8ArgueHP8X/d/g83QwO5Fb84Gz77A5TmwfT/gn/dRrbkFRv5cf8ZpgwOp5mMbRfiPPlrcBE5pTl8cvATPj/8OQDT+05nRt8ZBHg1oD7o8iL44o+Qfco6jW+bAXWucsm2U5SZLEwbLhdShahIknsjl1eWx7JDy/j88OeUmEqY3GUysyJmOX8UTGXlxfDVHZC8B25dBp1G1bnKrMIylmw5yaR+renVprkdghTCdUhyb6QySzJZHrucFUdXUGQs4rqO1/HQgIfoHFjP88HYoqzA2sd+ejvc9B70ts8KjIs2nqDEaOaJa7rbpT4hXIkk90bmdP5plscuZ1XcKowWI9d1uI4Z/WbQI7iHs0OrWnE2fD4FUmLg/xbXeLm8SzmTV8KnO0/zh0HhdG1Zs2mBhWgKJLk3AlprolKjWH54OZsSN+FucOeGzjcwo98MOjRvwH3NOfHw5e2QFWcdFdPzertVvfC3OLTWPDZe5pERoiqS3Buw/PJ8fjjxAyuPruRk3kmCvIKY2X8mU3tOdd48MLaK3wor7gRttk4r0HmM3ao+mVHIyuhEpg1rT7vg2k1XIISrk+TewFi0hejUaFbFreLX079Sai6lX0g/5o+cz4SOE5wzFW9NaA3RS2DtXAjqBLd/BSFd7Va90WzhiZW/08zTjYfH2a9eIVyNJPcGIi4njjWn1rDm1BqSC5Px8/BjcpfJTOk+hd4tejs7PNsUZcEPj8KR/0LXa2DKEvC271DMf66PIyYxl/f+NJCW/g38g04IJ5Lk7iRaa07knmBdwjp+Of0Lx3OOY1AGhrUexiMDH2F8+/ENv5Ve0fFf4fuHoSQHrv07DH8YDAa7niI6Ppv31h/n/waFc0N/uRtViMuR5F6PTBYTMekxbE7azIbEDcTnx6NQRLSM4Jmhz3Btx2sbfl96ZXlJ8POzELsKQntZb05qbf85XvJLjTy+IobwIF9euLGRfJMRwokkuTtYcmEyO1J2sD1lOzvP7KSgvAB3gzuDWw3mjl53ML79eEJ9Q50dZs2VFcKuRbDlLdAWGPssXPEoeNj/20ZRmYl7l0ZzJq+UlfePkPnahbCBJHc70lqTVJDE3vS9RKVGEZ0WTXJhMgAtfVsyrt04RrcbzYg2I/Dz9HNytLVUVgC7/w073oPiLOg1Ga77BwS2d8jpCstM/PmT3exNyOXdqREM7tAAZrQUohGQ5F4H+eX5xGbFcjDzIAcyDhCTEUN2aTYAAV4BDG45mGm9pjEibASdAzo7f/70usg+CdEfw77PrP3qXa+B0XOh3RCHnbJiYl84dSDX929gUyoI0YBJcreB2WImuTCZuNw4juUc42j2UY7mHCWxIPF8mXb+7RgZNpKIlhFEtIyga2BXDMq+FxTrXWk+HF0D+1fCid9AuVlvRBr5OIQ7dvrg3aeymfP17yTnlkhiF6IWJLmfpbUmpyyHxIJEEgsSOZ1/mvi8eOLz4zmVd4oyc9n5su3929MzuCe3dL2FPiF96NOiT8OafbEuck7DifXW0S9x68BcBs3DYcwzMOguaO7YUSol5Wbe/OUoS7adol2QL1/eN5yhnYIdek4hXJFNyV0pNQF4F3ADFmutX6203wv4FBgMZAG3aa3j7Rtq7WmtKTAWkFmcSUZJBunF6aQVp5FalMqZojOkFKaQUphCsan4/DEGZSCsWRgdAjowpPUQugZ2pUtgF7oGdqWZRzMnvhs7Mpsg8ygkRUFiFCTsgOwT1n3Nw2HIDOhzC7SNtPuwxsrSC0pZvuM0n+9KILuonDuHd+DpiT1ljnYhaqnavxyllBvwPnANkAREKaVWa61jKxSbAeRorbsqpaYCrwG3OSJgk8VEQXmB9WG0/ptflk9eeR55ZXnkluaSU5ZDblku2SXZZJdaH6Xm0ovqCvAKoE2zNrT3b8/wNsMJ9w8n3C+cdv7taOvfFi+3uq0Q1CBYLFCcCXmJ1nnUs09B1nFIi7UmdnO5tZxPMLQbCkNnQpdxENKtTkvf2eJ0VhGbj2ey+VgGG4+mY7JoxvdsxQOjOxPZUVrrQtSFLc2ioUCc1vokgFLqK+AmoGJyvwl44ezzb4D3lFJKa63tGCsASw8t5d29715yv7ebN4HegQR6BdLCuwWdAjoR7B1MqG8oIT4hhPqE0qpZK1r6tsTH3cfe4dmH1mAxgdloTb7nHsZSMJVY/zUWWRe/KCuEsnzrykaledZZGIszoSgTCtOh4AxYjBfW7x8GrXpDl7HQqi+ER0JwZ7slc601JUYzhaUmCspMZBeVk1FQRnp+KfFZxRxPL+BYWiEZBdaurvAgH6YN78DdIzrSMcRFvhUJ4WS2JPe2QGKF10nAsEuV0VqblFJ5QAsg0x5BVtT8SDwzszXNLNDMAr4W8D/7aGYBb10ClKA4c9l60m08n6Ly55OusO/CcufLao06f6z1uQHL+XIGNAoLCo0bFgzaggELbpgxYMEDk43RXagMTwqUH3kqgFzVnBxDJzLdh5BpaEG6CuGMoQ1nDK0pVV7WH0A6cBCs/0uTLnyXFT6X9dn/6LPbNWDRGosFzBaNWWvMFo3RZKHMZKHcbLlkjL6ebnRr6cfo7qH0DWvOVd1D6RTSrHGPJBKiAbIluVf1V1c549lSBqXUTGAmQPv2tRsX3S2gJ11Pd/rfWd3OPoDis4//BWCvhHFhPRXr1ZXK6fNJ6lyqV1iw9ldrZX2uMVi3K2ua18qAGTe0MmDBgEl5YFZumHHHrNwxKU9Myh2j8sJo8KRceVFm8KFM+VBu8KbE0IwSgx8mg+dl34UHcO6nrmz52agLnyplPcqgwKAUKHA3KNwMBtwM4Onmhqe7AU93A8083fDzdsfPy50gX09C/b1o6e9FkK8nBoMkciEczZbkngS0q/A6HEi5RJkkpZQ7EABkV65Ia/0R8BFAZGRkrbpsBl47Da6dVptDhRCiybBlCEQU0E0p1Ukp5QlMBVZXKrMauPvs8ynAekf0twshhLBNtS33s33os4CfsXaAfKy1PqSUegmI1lqvBpYAy5VScVhb7FMdGbQQQojLs2kQsdZ6DbCm0rZ5FZ6XArfaNzQhhBC11cjvjxdCCFEVSe5CCOGCJLkLIYQLkuQuhBAuSJK7EEK4IOWs4ehKqQzgtFNOXjchOGBahQauqb3npvZ+Qd5zY9JBa13t2pxOS+6NlVIqWmsd6ew46lNTe89N7f2CvGdXJN0yQgjhgiS5CyGEC5LkXnMfOTsAJ2hq77mpvV+Q9+xypM9dCCFckLTchRDCBUlyrwOl1ByllFZKhTg7FkdSSr2hlDqilNqvlPpOKRXo7JgcRSk1QSl1VCkVp5R62tnxOJpSqp1SaoNS6rBS6pBS6jFnx1RflFJuSql9Sqn/OjsWR5DkXktKqXZYFw1PcHYs9eBXoK/Wuj9wDHjGyfE4RIXF4CcCvYHblVK9nRuVw5mAJ7XWvYDhwMNN4D2f8xhw2NlBOIok99p7G/gLVSwn6Gq01r9orc8t7LoT62pcruj8YvBa63Lg3GLwLktrfUZrvffs8wKsya6tc6NyPKVUOHA9sNjZsTiKJPdaUErdCCRrrX93dixOcA+w1tlBOEhVi8G7fKI7RynVERgI7HJuJPXiHayNs0uv5t7I2bRYR1OklFoHtK5i17PAX4Fr6zcix7rc+9Vaf3+2zLNYv8Z/Xp+x1SObFnp3RUopP+A/wONa63xnx+NISqkbgHSt9R6l1Bhnx+MoktwvQWt9dVXblVL9gE7A70opsHZR7FVKDdVap9ZjiHZ1qfd7jlLqbuAGYLwLr49ry2LwLkcp5YE1sX+utf7W2fHUg5HAjUqpSYA30Fwp9ZnWepqT47IrGedeR0qpeCBSa90YJyCyiVJqAvAWMFprneHseBxFKeWO9YLxeCAZ6+Lwf9JaH3JqYA6krC2UZUC21vpxZ8dT38623OdorW9wdiz2Jn3uwhbvAf7Ar0qpGKXUh84OyBHOXjQ+txj8YWClKyf2s0YCdwLjzv6/jTnbohWNnLTchRDCBUnLXQghXJAkdyGEcEGS3IUQwgVJchdCCBckyV0IIVyQJHchhHBBktyFEMIFSXIXQggX9P9E8oI6Kj+/UAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x163516e2fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "''' 观察正态分布下，不同sigma值对累积分布函数的影响 '''\n",
    "\n",
    "%matplotlib inline\n",
    "import scipy.stats as sps\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x = np.linspace(-5, 5, 100)\n",
    "mu = 0\n",
    "for sigma in [0.5, 1.0, 2.0]:\n",
    "    y = sps.norm.cdf(x, mu, sigma)\n",
    "    plt.plot(x, y)\n",
    "    \n",
    "labels = ['sigma=0.2', 'sigma=1.0', 'sigma=5.0']\n",
    "plt.legend(labels)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
